No description has been provided for this image

Importance of 3D Forward Modelling for Gravity & Magnetic Field in Geophysics¶

Introduction¶

3D forward modeling in geophysics is crucial for simulating and understanding the subsurface distribution of physical properties such as density and magnetic susceptibility. Specifically, in gravity and magnetic field studies, 3D forward modeling helps predict how different subsurface structures would influence the observed gravitational and magnetic data, allowing for better interpretation of geological formations. These models are widely used in fields such as mineral exploration, tectonic studies, and environmental geophysics.

Finite Element Modelling (FEM) plays an important role in refining these simulations, especially when it comes to solving complex geometries and inhomogeneities in the subsurface. Here we discuss the significance of 3D forward modeling for gravity and magnetic field analysis, with a particular focus on the use of FEM.

Importance of 3D Forward Modelling¶

  1. Subsurface Characterization:

    • 3D forward modeling enables detailed characterization of subsurface geological structures by simulating gravity and magnetic responses for various geological settings.
    • It provides insights into the location, depth, and extent of anomalies caused by mineral deposits, tectonic features, and other subsurface structures.

  2. Predictive Power:

    • Predicts the effect of complex subsurface structures on the gravity and magnetic fields. This predictive capability allows geophysicists to assess potential targets for exploration before expensive drilling operations.
    • By comparing model predictions with actual measured data, geophysicists can refine models to better match reality.

  3. Complex Geological Environments:

    • Natural geological environments are often highly irregular and complex. 3D forward modeling allows geophysicists to handle such complexities and better understand the relationship between surface measurements and subsurface features.
    • These models accommodate lateral and vertical variations in physical properties such as density and susceptibility, which are essential for interpreting non-homogeneous media.

  4. Enhanced Accuracy:

    • Modern 3D models can incorporate real-world data such as terrain, subsurface density, and magnetic susceptibility variations, providing more accurate predictions of the measured fields.
    • This improves the precision of geological interpretations, especially in areas where 2D or 1D models would oversimplify the subsurface conditions.

Finite Element Modelling (FEM) in Gravity & Magnetic Field Studies¶

Finite Element Modelling (FEM) is a numerical technique that is particularly suited for solving partial differential equations (PDEs) over complex geometries, making it a powerful tool for 3D forward modeling in gravity and magnetic field studies.

Key Contributions of FEM:¶

  1. Handling Irregular Boundaries:

    • FEM is excellent for modeling irregular geological boundaries, which are common in gravity and magnetic studies. This is essential for achieving more realistic representations of subsurface structures.
    • Compared to traditional methods like finite difference, FEM offers more flexibility when dealing with complex geometries such as faults, folds, or intrusive bodies.

  2. Accurate Representation of Heterogeneous Media:

    • The subsurface is rarely homogeneous, with varying material properties such as density and magnetic susceptibility. FEM allows for the discretization of the model into smaller elements, each of which can have different physical properties.
    • This enhances the accuracy of modeling in heterogeneous regions, where conventional methods may struggle to provide precise solutions.

  3. Adaptive Mesh Refinement:

    • FEM techniques allow for adaptive mesh refinement, which improves accuracy in areas with high gradients (e.g., near faults or edges of intrusions) by using finer meshes where necessary and coarser meshes elsewhere.
    • This approach optimizes computational resources and enhances the precision of field calculations.

  4. Efficient Handling of Boundary Conditions:

    • Complex boundary conditions such as varying topography or open boundaries can be effectively handled using FEM. This is particularly important for realistic gravity and magnetic forward modeling where surface and subsurface conditions vary significantly.

  5. Scalability to Larger Models:

    • FEM is well-suited for parallel computation, making it scalable for large-scale geophysical models that involve millions of degrees of freedom. This is particularly beneficial when working with large datasets or high-resolution models required for modern exploration techniques.

Applications of 3D Forward Modelling with FEM¶

  1. Mineral Exploration:

    • 3D forward modeling of gravity and magnetic fields is widely used in mineral exploration to locate ore bodies and estimate their size, depth, and composition. FEM helps to refine these models, especially in areas with complex subsurface geology.

  2. Tectonic Studies:

    • In tectonic settings, FEM-based 3D forward modeling helps to simulate the effects of large-scale geological structures such as subduction zones, fault systems, and crustal deformation on gravity and magnetic fields.

  3. Environmental Geophysics:

    • In environmental studies, FEM allows for precise modeling of contaminant plumes or other subsurface features that affect gravity and magnetic measurements, aiding in the identification of pollution or buried waste.

Conclusion¶

3D forward modeling in gravity and magnetic field studies provides invaluable insights into subsurface geology. When combined with Finite Element Modelling, the accuracy and flexibility of these models are significantly enhanced. FEM offers superior capabilities in handling complex geometries, heterogeneous media, and boundary conditions, making it an essential tool for advanced geophysical exploration and research.

By leveraging 3D forward modeling and FEM, geophysicists can achieve more accurate interpretations, optimize exploration strategies, and reduce the uncertainty in subsurface investigations.

In [1]:
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import Forward_Model as fm
In [2]:
# Parameters
L = 1000  # Size of the 3D grid (meters)
N = 30   # Number of points in each dimension
cylinder_radius = 200  # Radius of the cylinder (meters)
cylinder_length = 500  # Length of the cylinder along the Z-axis (meters)
cylinder_center = np.array([L/2, L/2])  # Center of the cylinder in the X-Y plane
susceptibility_cylinder = 0.04  # SI
susceptibility_background = 0.001  # SI
susceptibility, X, Y, Z = fm.create_3d_cylinder(cylinder_radius, cylinder_length, susceptibility_cylinder, susceptibility_background, L = 1000, N = 30)
In [3]:
fig = fm.plot_3d_subsurface(susceptibility, X, Y, Z)
fig.show()
In [13]:
# Earth's magnetic field parameters
I = np.radians(49)  # Magnetic inclination in radians
D = np.radians(-10.2)  # Magnetic declination in radians
B_0 = 31000  # Earth's magnetic field strength in nT (assumed)
In [14]:
delta_T_sim = fm.create_3d_forward_model(I, D, B_0, susceptibility, L, N)
In [15]:
fm.plot_forward_model(delta_T_sim, X, Y)
No description has been provided for this image